---
name: computational-strategy
description: >
  Direct the computational strategy subdomain — route questions about algorithmic game theory,
  computational complexity of equilibria, behavioral game theory, bounded rationality,
  learning in games, multi-agent reinforcement learning, and AI-era game theory to the right
  specialist skill. Use when computational limits, bounded rationality, or AI agents are central.
metadata:
  author: nirav
  version: "1.0"
compatibility: Designed for Claude Code
allowed-tools: Read Glob
---

# Computational Strategy Director — The Realist

The department head for computational strategy within the game-theory domain. This subdomain asks three questions classical game theory ignores: (1) Can equilibria actually be *computed*? (2) Do real humans *play* equilibrium? (3) Can agents *learn* their way to equilibrium? Routes questions to the right specialist, defines the learning order, and resolves conflicts between computational, behavioral, and learning perspectives.

## Routing Logic

When a question arrives in this subdomain, classify it and route accordingly:

| Question Pattern | Route To | Why |
|-----------------|----------|-----|
| PPAD-completeness, complexity of Nash, can we compute equilibria? | `algorithmic-game-theory` | Computational complexity |
| Price of anarchy, price of stability, efficiency of selfish routing | `algorithmic-game-theory` | Efficiency of equilibria |
| Congestion games, potential games, Braess paradox | `algorithmic-game-theory` | Network/algorithmic games |
| Algorithmic mechanism design, computational mechanism design | `algorithmic-game-theory` | Intersection with mechanism design |
| Level-k thinking, cognitive hierarchy, depth of reasoning | `behavioral-game-theory` | Bounded rationality models |
| QRE, quantal response, noisy best response | `behavioral-game-theory` | Stochastic choice models |
| Social preferences, fairness, inequality aversion, reciprocity | `behavioral-game-theory` | Non-standard preferences |
| Experimental game theory, lab results, real humans playing games | `behavioral-game-theory` | Empirical evidence |
| Fictitious play, no-regret learning, regret matching | `learning-in-games` | Learning algorithms |
| Multi-agent reinforcement learning (MARL), self-play, AlphaGo | `learning-in-games` | AI/ML game theory |
| Mean field games, large population limits | `learning-in-games` | Continuum approximations |
| LLM alignment, RLHF, AI safety as game theory | `learning-in-games` | Frontier AI applications |
| "How would real people play this?", "Is the Nash realistic?" | `behavioral-game-theory` first, then `learning-in-games` | Behavioral prediction |
| "Can a computer solve this game?" | `algorithmic-game-theory` | Complexity assessment |

### Multi-Skill Questions

Some questions need more than one skill. Load them in this priority:

1. `algorithmic-game-theory` — can the equilibrium be computed? What are the computational constraints?
2. `behavioral-game-theory` — do real humans play equilibrium? If not, what do they play?
3. `learning-in-games` — can agents learn to play equilibrium? Which algorithms converge?

This order reflects increasing sophistication: first assess what's computable, then what's empirically observed, then what dynamics lead to observed behavior.

**Example multi-skill question**: "Will users on my platform converge to efficient behavior?"
1. `algorithmic-game-theory` → Does the game have a potential function? If so, best-response dynamics converge. If not, convergence is not guaranteed.
2. `behavioral-game-theory` → Real users have bounded rationality — level-k reasoning, social preferences, and anchoring will shape early behavior
3. `learning-in-games` → With repeated interaction, no-regret learning leads to coarse correlated equilibrium. The convergence rate and path depend on the learning algorithm.

## Curriculum Order

For learning or progressive loading:

1. **Algorithmic Game Theory** (computational foundation) — What can and can't be computed. PPAD-completeness sets hard limits on equilibrium computation. Price of anarchy quantifies efficiency loss. Establishes why we need alternatives to "just compute Nash."

2. **Behavioral Game Theory** (empirical foundation) — What humans actually do. Level-k thinking, QRE, and social preferences explain systematic deviations from Nash. Grounds theory in experimental evidence.

3. **Learning in Games** (dynamic foundation) — How agents (human or AI) reach equilibrium through repeated interaction. Connects classical convergence results to modern MARL and AI training.

### Level Progression
- **Foundational**: Algorithmic Game Theory, Behavioral Game Theory
- **Intermediate**: Learning in Games
- **Advanced**: (future) Mean Field Games, AI Safety as Game Theory, Quantum Game Theory

## Conflict Resolution

When child skills give contradictory guidance:

| Conflict | Resolution | Reason |
|----------|-----------|--------|
| Algorithmic GT says "Nash is PPAD-hard to compute" but learning GT says "no-regret learning converges" | Both correct but converge to different concepts — no-regret converges to coarse correlated equilibrium (CCE), which is weaker than Nash. Present the distinction: CCE is computable, Nash is not (in general) | Different solution concepts have different computational properties |
| Behavioral GT predicts level-2 play but learning GT predicts convergence to Nash after 1000 rounds | Time scale matters — behavioral predictions apply to early/few-shot play; learning predictions apply to repeated interaction. Both can be correct for different time horizons | Short-run ≠ long-run behavior |
| Nash says defect in PD but behavioral GT shows 40-60% cooperation in experiments | Present both — Nash is the rational benchmark, behavioral evidence shows humans deviate due to social preferences, reciprocity, and bounded rationality. Neither is "wrong" — they answer different questions | Normative (what should you do?) vs. descriptive (what do people do?) |
| Price of anarchy is large but learning dynamics converge to efficient outcomes | PoA measures worst-case. Learning dynamics may avoid worst-case equilibria. Report both — PoA as a bound, dynamics as a prediction | Worst-case vs. typical-case analysis |

**General rule**: Classical Nash analysis provides the benchmark. Behavioral GT provides the empirical correction. Learning GT provides the dynamic story. All three perspectives are needed for a complete picture.

## Scope Boundaries

**This director handles**: All questions involving computational limits on game-theoretic reasoning, human deviations from rational play, learning and adaptation in strategic settings, and AI/ML applications of game theory.

**Escalate to the orchestrator when**:
- The question assumes fully rational, computationally unconstrained players → Strategic Foundations
- The question is about designing rules/institutions → Mechanism Design
- The question is about biological populations → Evolutionary Dynamics
- The question is about strategic information design → Information Economics